The SAT started as something close to an IQ test. If you have the time, this website has an interesting history of the SAT:
http://www.erikthered.com/tutor/sat-act-history.htmlOver the years it has evolved into more of an achievement test. The College Board is supposed to change the SAT again in a year or so to make it even more achievement-like.
You can prep and you can raise your score, even if the College Board says you cannot. However, for most kids, there are limits to how much they can raise their score. If you start out at a 1500 (out of 2400), maybe you can raise the score to 1700. If you begin at 2000, it is reasonable that you could prep and score a 2200. It would be very rare for a kid to make a leap of 500 or 600 points. While many folks on this forum may say that the SAT has a low ceiling or it is easy to score above 2000, decades of testing doesn't seem to show this. If it was easy to prep and raise your score a lot, kids would do this and the test would be renormed (of course it has been renormed - the other direction due to dropping test scores).
If you have a good solid background in math and have read plenty of literature and publications like the New York Times and the Economist, you will do well on the SAT. Of course, many kids in the US don't have great math instruction and they haven't read literature or publications with rich vocabulary, so they struggle with the SAT.